The simulation of phase diagrams for polymer blends at various pressures

A procedure is described for the simultaneous prediction of the binodal and spinodal curves of polymer mixtures at various pressures using a form of the equation-of-state theory of Flory and co-workers. The results of the calculation are compared with experimental results for the effect of pressure on the cloud points of both oligomer mixtures showing upper critical behavior and polymer mixtures showing lower critical behavior. The procedure successfully predicts the sign of the effect and its magnitude within the experimental and theoretical uncertainties for the systems studied.     

Membrane formation via phase separation induced by penetration of nonsolvent from vapor phase. I. Phase diagram and mass transfer process

The isothermal phase diagram for poly(vinylidene fluoride)/dimethyl formamide/water system was derived. The binodal and spinodal were calculated based on the Flory–Huggins theory and the calculated binodal was approximately in agreement with the experimental data of the cloud points. The isothermal crystallization line was also obtained according to the theory of melting point depression. Mass transfer of the three components during membrane formation by the precipitation from the vapor phase has been analyzed. During this process, phase separation of the polymer solution is induced by the penetration of water vapor in the solution. The calculated result on the changes of the cast film weights indicated the good agreement with the experimental data. The time‐course of the polymer concentration profile in the film was calculated for various cases of different humidity of the vapor phase and different initial polymer concentration. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 159–170, 1999     

液液平衡和会溶现象

提出了液体混合的通用Gibbs自由能模型,据此建立了液液平衡的双节线、旋节线和临界点方程.这些方程不仅适用于小分子液体混合物,而且亦适用于高分子溶液.计算结果表明,它们能满意地描述各种类型的液液平衡及其会溶现象.     

Theoretical representation of shear and pressure influence on the phase separation behavior of PVME/PS mixture

In the framework of lattice fluid model, the Gibbs energy and equation of state are derived by introducing the energy (E_s) stored during flow for polymer blends under shear. From the calculation of the spinodal of poly(vinyl methyl ether) (PVME) and polystyrene (PS) mixtures, we have found the influence of E_s on equation of state in pure component is inappreciable, but it is appreciable in the mixture. However, the effect of E_s on phase separation behavior is extremely striking. In the calculation of spinodal for the PVME/PS system, a thin, long and banana miscibility gap generated by shear is seen beside the miscibility gap with lower critical solution temperature. Meanwhile, a binodal coalescence of upper and lower miscibility gaps is occurred. The three points of the three-phase equilibrium are forecasted. The shear rate dependence of cloud point temperature at a certain composition is discussed. The calculated results are acceptable compared with the experiment values obtained by Higgins et al. However, the maximum positive shift and the minimum negative shift of cloud point temperature guessed by Higgins are not obtained. Furthermore, the combining effects of pressure and shear on spinodal shift are predicted.     

Effects of molecular weight distribution on the spinodal temperature of polymer mixtures

The effects of molecular weight distribution on the phase stability of polymer mixtures were explored theoretically and experimentally. Based on the lattice‐fluid theory and volume‐fluctuation thermodynamics, the spinodal conditions for a lattice‐fluid mixture of two polymers with molecular weight distribution were derived. The results indicated that the phase stability of a polymer mixture decreases by increasing the molecular weight distribution of polymers in the blend. To confirm the theoretical results with experiments, the changes in the spinodal temperatures of poly(ethyl methacrylate)/polystyrene (PEMA/PS) blends and tetramethyl polycarbonate/polystyrene (TMPC/PS) blends were examined when each component has a different molecular weight distribution. When the weight‐average molecular weight of each component is the same, a blend composed of polymers having broad molecular weight distribution always exhibited lower phase separation than that composed of polymers having narrow molecular weight distribution at the same blend composition. Copyright © 2004 Society of Chemical Industry     

Zum thermodynamischen verhalten von polystyrol (PS)/poly(vinylmethylether) (PVME)-blends

The polymer blend system PS/PVME shows a phase behaviour with lower critical separation temperature (LCST behaviour), which was simulated and discussed with the help of the model of Dee and Walsh as well as by means of the continuous thermodynamics. The results show that the Prigogine equation of state is able to fit advantageously the real PVT behaviour in the polymer melt. The spinodal curve used by the Dee/Walsh model gives a very good conformity with the results of the cloud point measurements. The model simulations show an increase of the compatibility of this polymer system with increasing pressure. By means of the continuous thermodynamics the influence of polydispersity on the phase behaviour of the blend system could be made clear. A marked shift of the critical point from minimum is seen because of the broad molecular mass distribution of PVME.     

Phase separation of poly (methyl methacrylate) / poly (styrene-co-acrylonitrile) blends in the presence of silica nanoparticles

The effects of silica nanoparticles on the phase separation of poly (methyl methacrylate)/poly (styrene-co-acrylonitrile) (PMMA/SAN) blends are studied by the rheological method. The binodal temperatures of near-critical compositions were obtained by the gel-like behavior during spinodal decomposition, which is a character of polymer blends with co-continuous morphology. The shifted Cole–Cole plot method was introduced to determine the binodal temperatures of off-critical compositions based on the appearance of shoulder-like transition in the terminal regime of blends with droplet morphology. Such method is found also applicable in nanoparticle filled polymer blends. Moreover, a new method to determine the spinodal temperature from Fredrickson-Larson mean field theory was suggested, where the concentration fluctuation's contribution to the storage modulus is used instead of the whole dynamic moduli. This method was also successfully extended to nanoparticle filled polymer blend. The influences of the concentration and the average diameter of silica particles on the phase separation temperature were studied. It was found that the small amount of the silica nanoparticles in PMMA/SAN blends will significantly change the phase diagram, which is related to the selective location of silica in PMMA. The comparisons with thermodynamic theory of particle-filled polymer blends are also discussed.     

Analysis of nonsolvent–solvent–polymer phase diagrams and their relevance to membrane formation modeling

Calculations have been carried out, based on Flory–Huggins solution theory, to analyze the behavior of the ternary nonsolvent–solvent–polymer phase diagram for typical membrane-forming systems. Consideration is given to the behavior of the spinodal as well as binodal curves, tie-line slopes, and critical points as a function of various parameters, most especially those related to the concentration dependency of the interaction parameters. Implications regarding membrane structure formation are discussed, and the suitability of different functional forms for the interaction parameter concentration dependence is also analyzed. The net result of these calculations is to demonstrate the importance of the various parameters in controlling the phase-diagram behavior and particularly to show the critical role of the concentration dependence of the solvent–polymer interaction parameter in affecting the nature of the miscibility gap.     

Comparison of the phase behaviour of the liquid-crystalline polymer/poly(methyl methacrylate) and poly(vinyl acetate)/poly(methyl methacrylate) blends

The phase behaviour of blends of a liquid-crystalline polymer (LCP) and poly(methyl methacrylate) (PMMA), as well as the phase state of blends of PMMA and poly(vinyl acetate) (PVA) has been investigated using light scattering and phase-contrast optical microscopy. The blends of LCP and PMMA have been obtained by coagulation from ternary solutions. The cloud point curves were determined. It was established that both pairs demix upon heating, ie have an LCST. In the region of intermediate composition, the phase separation proceeds according to a spinodal mechanism; however for LCP/PMMA blends, the decomposition proceeds according to a non-linear regime from the very onset. In the region of small amounts of LCP, the phase separation follows a mechanism of nucleation and growth. For PMMA/PVA blends, the spinodal decomposition proceeds according to a linear regime, in spite of the molecular mobility that PVA chains develop at lower temperatures. Only after prolonged heat treatment does the process transit to a non-linear regime. The data show a similarity between the phase behaviour of blends of liquid-crystalline and of flexible amorphous polymers. The distinction consists of the absence of a linear regime of decomposition for LCP-PMMA blends. © 1999 Society of Chemical Industry     

Phase separation in polystyrene-poly(vinylmethylether) blends: a a fluorescence emission analysis

Fluorescence emission of labels appears to be a new technique for the investigation of the LCST behaviour of polystyrene-poly(vinylmethylether) (PS-PVME) blends. Indeed, heating ternary blends of PVME/PS/labelled PS results in sharp increases in the fluorescence intensity, which occur simultaneously with their phase separation. Specific interactions between the anthracenic units of the labelled PS and the ether functions of PVME, are responsible for the fluorescence quenching, which occurs in the compatible blends. Quenching drops as phase separation proceeds, because of the lowering of the probability for label-PVME interactions in the two-phase state. By relating the phase separation curves obtained in this way to those acquired by the classical light scattering method, it is shown that fluorescence experiments may allow determination of both spinodal and binodal curves, provided that heating rate is appropriate.     

Formation of polyurethane membranes by immersion precipitation. i. liquid–liquid phase separation in a polyurethane/DMF/water system

Liquid–liquid phase separation phenomena of polyurethane/DMF/water were studied. Two polyurethanes having different hydrophobicity were synthesized by varying the polyol components. The cloud-point curves for the ternary system of polyurethane/DMF/water were determined by the titration method. A small amount of water is needed to induce liquid–liquid demixing, and the region of the homogeneous phase is enlarged with increased hydrophilicity of the polyurethane. We measured the interaction parameters, and calculated the binodal and spinodal curves based on the thermodynamics of polymer solutions. The light transmission experiment showed that precipitation time increased with the higher content of DMF in a coagulation bath. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2377–2384, 1999     

Treatment of poly(styrene‐co‐methacrylic acid)/poly(4‐vinylpyridine) blends in solution under liquid–liquid phase‐separation conditions. A new method for phase‐separation data attainment from viscosity measurements

Phase diagrams are contributed for polymer mixture systems in solution. One polymer has proton‐acceptor character and the other has growing proton‐donor nature, which is reflected in the phase diagrams. Usually, these diagrams are obtained from size‐exclusion chromatographic (SEC) measurements. A totally novel application, which is exposed in this report, is the construction of the phase diagram from the viscometric experiments of polymer mixtures. The evaluated binodal or cloud‐point isotherms so built agree well with those from SEC. The results indicate an augmentation in the dimensions of donor polymer B, in the presence of acceptor polymer C, intensifying with the concentration of C, which is interpreted as an B‐C association growing as the number of hydrogen bonds increases. An increment in the Huggins constant for BC, as the proportion of methacrylic acid in the donor copolymer increases, means an augmentation in the interaction for BC, indicating an extension of compatibility. Viscometric experiments evidence hydrogen bonds, intensifying as greater proportion of donor groups has polymer B, equal to that observed in the phase diagrams. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:5039–5049, 2006     

Cloud point curves for poly(vinyl methyl ether) and monodisperse polystyrene mixtures

The compatibility behaviour of poly(vinyl methyl ether) (PVME) and monodisperse polystyrene (PS) is studied for solution cast films. The molecular weight of monodisperse PS ranges from 2100 to 2 000 000 whereas the PVME used is polydisperse and has weight-average molecular weight of 51 500. When cast from toluene solution, the mixtures undergo phase separation at elevated temperatures. The cloud point curves move to markedly lower temperatures with increasing molecular weight which is similar to the lower critical solution temperature (LCST) behaviour for polymer solutions. They move to lower temperatures until the molecular weight of PS reaches about 51 500.The effect of molecular weight distribution on the cloud point of equal amounts of PS and PVME mixtures simulated by mixing two monodisperse polystyrenes of different molecular weight for PS part is accurately predicted by using weight-average molecular weight for PS in this range. However, if the molecular weight of PS exceeds about 110 000 the molecular weight dependence of cloud point temperature is reversed and the prediction for polydisperse polymer by using weight-average molecular weight fails. This phenomenon is discussed from several viewpoints including the possibility of the effect of chain entanglement.Mixtures of PVME and PS of M_w = 20 400 were also cast from an ‘incompatible’ solvent, trichloroethylene. Compatibility is found to be dependent on composition and even phase-separated samples show at least one cloud point, indicating at least partial mixing of the two polymers. Finally, it is demonstrated that crosslinking of compatible films can be achieved by electron irradiation to form true interpenetrating networks. The cloud point temperatures are increased drastically after crosslinking.     

Generalized Flory–Huggins model for heat‐of‐mixing and phase‐behavior calculations of polymer–polymer mixtures

An extended and generalized Flory–Huggins model for calculating the heats of mixing and predicting the phase stability and spinodal diagrams of binary polymer–polymer mixtures is presented. In this model, the interaction parameter is considered to be a function of both temperature and composition. It is qualitatively shown that the proposed model can calculate the heats‐of‐mixing curves containing exothermic, endothermic, and S‐shaped or sigmoidal types and predict the spinodals, including the upper and lower critical solution temperatures, and closed‐loop miscibility regions. Using experimental results of analog calorimetry for four polymer mixtures of polystyrene/poly(vinyl chloride) (PS/PVC), polycarbonate (PC)/poly(ethylene adipate) (PEA), polystyrene/poly(vinyl acetate) (PS/PVAc), and ethylene vinyl acetate copolymer (EVA Co)/chlorinated polyethylene (CPE), the capabilities of the proposed functionality for the interaction parameter was studied. It is shown that this function can be used satisfactorily for the heat‐of‐mixing calculations and phase‐behavior predictions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1328–1340, 2000     

Lower critical solution temperature of linear PNIPA obtained from a Yukawa potential of polymer chains

The lower critical solution temperature (LCST) behavior of a linear poly(N‐isopropylacrylamide) (PNIPA) in water is thought to result from the polymer–polymer attractive interaction. This polymer–polymer attraction is modeled by a temperature‐dependent Yukawa attractive potential, with Yukawa parameters determined by fitting the theoretical phase diagram for a pure Yukawa fluid to the experimental lower consolute boundary for a PNIPA–water solution. The predicted coexistence curve for the PNIPA–water mixtures in the temperature‐polymer volume fraction plane is reasonably close to the experimental cloud point data for the PNIPA–water system. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1971–1976, 2000     

Kinetics of pressure-induced phase separation in polystyrene + acetone solutions at high pressures

The kinetics of pressure-induced phase separation in solutions of polystyrene (M_w = 129,200; PDI = 1.02) in acetone has been studied using time- and angle-resolved light scattering. A series of controlled pressure quench experiments with different quench depths were conducted at different polymer concentrations (4.0%, 5.0%, 8.2% and 11.4% by mass) to determine the binodal and spinodal boundaries and consequently the polymer critical concentration. The results show that the solution with a polymer concentration 11.4 wt% undergoes phase separation by spinodal decomposition mechanism for both the shallow and deep quenches as characterized by a maximum in the angular distribution of the scattered light intensity profiles. Phase separation in solutions at lower polymer concentrations (4.0, 5.0 and 8.2 wt%) proceeds by nucleation and growth mechanism for shallow quenches, but by spinodal decomposition for deeper quenches. These results have been used to map-out the metastable gap and identify the critical polymer concentration where the spinodal and binodal envelops merge.The time scale of new phase formation and growth as (accessed) from the time evolution of scattered light intensities is observed to be relatively short. The late stage of phase separation is entered within seconds after a pressure quench is applied. For the systems undergoing spinodal decomposition, the characteristic wave number qm corresponding to the scattered light intensity maximum Im was analyzed by power-law scaling according to qm∼t−α and Im∼tβ. The results show β≈2α. The domain size is observed to grow from 4 μm to 10 μm within 2 s for critical quench, but about 9 s for off-critical quenches. The domain growth displays elements of self-similarity.     

A framework for morphological evolution vis-à-vis phase transitions in polymer solutions

When a polymer crystallizes from solution, it is well known that the resulting morphology depends on whether any liquid–liquid phase separation (LLPS) has preceded crystallization. In addition to the dense morphology that results when crystallization occurs directly from a homogeneous solution, at least three other distinctly different morphologies are produced if crystallization follows LLPS. Although much work has been reported in this regard, a framework that can relate the path that a process might follow across a phase diagram to the consequent morphology is lacking. We report here the fundamental elements of a simple thermodynamic framework that serves to identify the driving forces that produce these different morphologies. It is based on identification of the nucleating phase, if any, in LLPS and coupling it with the domain in which nucleation of crystallization occurs. The essential elements of the framework for morphological evolution are demonstrated by relating the sequence of phase transitions to the morphology which can result in the crystallized polymer when a polymer solution is cooled from a homogeneous state at a high temperature. Four distinctly different morphologies are shown to evolve, depending on whether crystallization occurs (a) directly from a homogeneous solution (dense); (b) following binodal liquid–liquid phase separation, LLPS, with nucleation of the polymer-rich phase (GMP—globular microporous); (c) following spinodal LLPS (FMP—fibrillar microporous); or (d) following binodal LLPS with nucleation of the solvent-rich phase (CTMP—cell-tunnel microporous). An important implication of the framework is that a predictable sequence of “dense → GMP → FMP → CTMP → dense” morphologies has to arise with increase in overall polymer concentration in such solutions. The framework also serves to identify conditions, such as passage through specific temperature/concentration regions in the phase diagram, that would increase the likelihood of forming mixed or coexisting morphologies. However, it is still necessary to develop appropriate kinetic models to predict sizes of the morphological components within each of the four morphologies. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 1343–1355, 1999     

Effect of coagulation bath temperature on formation mechanism of poly(vinylidene fluoride) membrane

Effects of coagulation bath temperature on the membrane formation mechanism and the morphologies of the formed membranes were studied. The binodal and spinodal lines in the phase diagrams of water/DMAc/Poly(vinylidene fluoride) (PVDF) were calculated based on the thermodynamics equations of membrane formation, and the gel phase boundaries of the systems at 25°C and 60°C were determined via cloud point measurement. The obtained ternary phase diagrams of water/DMAc/PVDF contain three regions: the one‐phase region, the liquid–liquid two‐phase region, and the gel region. In the phase diagrams, the liquid–liquid demixing line (binodal) is located inside the gelation line. At low temperature, there exists a wide region between gelation line and binodal line. Gelation could occur in the absence of liquid–liquid demixing, and becomes the dominant membrane formation mechanism. At high temperatures (60°C), however, the gelation line approaches the binodal line, which results in a much smaller gelation zone. The kinetics of the solvent out‐flux and water influx were enhanced, liquid–liquid demixing is the dominant mechanism. The membrane formation mechanisms at different temperature were confirmed by the light transmission measurements during membrane forming process and the morphologies of the membranes examined by SEM imaging. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008.     

Effects of cooling temperature and aging treatment on the morphology of nano‐ and micro‐porous poly(ethylene‐co‐vinyl alcohol) membranes by thermal induced phase separation method

Poly(ethylene‐co‐vinyl alcohol) (EVOH 32) / 1,3‐propanediol mixtures are processed by thermally induced phase separation for the formation of porous membranes. The crystallization line was determined both by the cloud‐point and DSC methods. Two precursor solution compositions, four quench temperatures and various aging times were explored. It is found possible to generate both polymer‐crystallization controlled morphologies (for high quenches and/or sufficiently aged dopes), especially globular microporous ones, and novel nano‐scale porous morphologies dominated by intra‐binodal phase separation (for low quenches and limited or no precursor solution aging). Structural characterization of the membranes was accomplished via application of scanning electron microscopy and wide angle X‐ray diffraction. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40374.     

Morphology and properties control on rubber-epoxy alloy systems

Morphology and properties of polymer alloys can be controlled by thermody-namlcally reversible (structure freeze-in) or irreversible (structure lock-in) processes by simultaneously manipulating miscibility, mechanisms of phase separation, glass transition temperature (structural relaxation), and cure kinetics of polymer systems. Using phase diagrams consisting of binodal and spinodal curves, the morphology of epoxy/CTBN (carboxyl-terminated butadiene acryloni-trile copolymer) systems can be controlled by the mechanism of nucleation and growth or by spinodal decomposition via simultaneously manipulating the kinetic processes of phase separation and curing reactions. We have found that the particle size of the rubber reinforcement in epoxies is affected by the mechanisms of phase separation. Phase separation by nucleation and growth gives larger rubber particles than the corresponding phase separation by spinodal decomposition. This contrast in the morphology development is the consequence of controlling phase separation through chemorheological behavior. Medication of the phase separation kinetics in epoxy/CTBN systems was extremely effective at altering both morphology and properties of these alloys. This technique offers a means to shift the glass transition temperature of the rubber-rich phase drastically without reducing the glass transition temperature of the epoxy-rich phase significantly. Such control over morphology is the key to ultimately controlling material properties. This morphology manipulation allows us to tailor the mechanical properties of alloy systems.